{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ITensorMPS\n",
    "using ITensors\n",
    "using Plots\n",
    "using DelimitedFiles\n",
    "using ITensorEntropyTools\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find Ground State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After sweep 1 energy=-20.867741989395604  maxlinkdim=10 maxerr=2.00E-03 time=0.308\n",
      "After sweep 2 energy=-20.883136377437207  maxlinkdim=20 maxerr=2.92E-08 time=0.011\n",
      "After sweep 3 energy=-20.883211945234933  maxlinkdim=35 maxerr=9.97E-11 time=0.017\n",
      "After sweep 4 energy=-20.883211999867164  maxlinkdim=29 maxerr=9.90E-11 time=0.015\n",
      "After sweep 5 energy=-20.88321199988478  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n",
      "After sweep 6 energy=-20.88321199988479  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n",
      "After sweep 7 energy=-20.883211999884793  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n",
      "After sweep 8 energy=-20.883211999884786  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n",
      "After sweep 9 energy=-20.88321199988477  maxlinkdim=29 maxerr=8.24E-11 time=0.016\n",
      "After sweep 10 energy=-20.883211999884747  maxlinkdim=29 maxerr=8.24E-11 time=0.017\n",
      "After sweep 11 energy=-20.88321199988477  maxlinkdim=29 maxerr=8.24E-11 time=0.020\n",
      "After sweep 12 energy=-20.88321199988479  maxlinkdim=29 maxerr=8.24E-11 time=0.022\n",
      "After sweep 13 energy=-20.883211999884757  maxlinkdim=29 maxerr=8.24E-11 time=0.017\n",
      "After sweep 14 energy=-20.8832119998848  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n",
      "After sweep 15 energy=-20.883211999884804  maxlinkdim=29 maxerr=8.24E-11 time=0.015\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-20.883211999884804, MPS\n",
       "[1] ((dim=2|id=346|\"Link,l=1\"), (dim=2|id=584|\"S=1/2,Site,n=1\"))\n",
       "[2] ((dim=4|id=872|\"Link,l=2\"), (dim=2|id=407|\"S=1/2,Site,n=2\"), (dim=2|id=346|\"Link,l=1\"))\n",
       "[3] ((dim=2|id=816|\"S=1/2,Site,n=3\"), (dim=8|id=999|\"Link,l=3\"), (dim=4|id=872|\"Link,l=2\"))\n",
       "[4] ((dim=2|id=381|\"S=1/2,Site,n=4\"), (dim=16|id=586|\"Link,l=4\"), (dim=8|id=999|\"Link,l=3\"))\n",
       "[5] ((dim=2|id=161|\"S=1/2,Site,n=5\"), (dim=22|id=612|\"Link,l=5\"), (dim=16|id=586|\"Link,l=4\"))\n",
       "[6] ((dim=2|id=595|\"S=1/2,Site,n=6\"), (dim=27|id=198|\"Link,l=6\"), (dim=22|id=612|\"Link,l=5\"))\n",
       "[7] ((dim=2|id=131|\"S=1/2,Site,n=7\"), (dim=29|id=30|\"Link,l=7\"), (dim=27|id=198|\"Link,l=6\"))\n",
       "[8] ((dim=2|id=253|\"S=1/2,Site,n=8\"), (dim=29|id=807|\"Link,l=8\"), (dim=29|id=30|\"Link,l=7\"))\n",
       "[9] ((dim=2|id=658|\"S=1/2,Site,n=9\"), (dim=29|id=560|\"Link,l=9\"), (dim=29|id=807|\"Link,l=8\"))\n",
       "[10] ((dim=2|id=429|\"S=1/2,Site,n=10\"), (dim=27|id=573|\"Link,l=10\"), (dim=29|id=560|\"Link,l=9\"))\n",
       "[11] ((dim=2|id=994|\"S=1/2,Site,n=11\"), (dim=22|id=300|\"Link,l=11\"), (dim=27|id=573|\"Link,l=10\"))\n",
       "[12] ((dim=2|id=796|\"S=1/2,Site,n=12\"), (dim=16|id=634|\"Link,l=12\"), (dim=22|id=300|\"Link,l=11\"))\n",
       "[13] ((dim=2|id=477|\"S=1/2,Site,n=13\"), (dim=8|id=796|\"Link,l=13\"), (dim=16|id=634|\"Link,l=12\"))\n",
       "[14] ((dim=2|id=382|\"S=1/2,Site,n=14\"), (dim=4|id=332|\"Link,l=14\"), (dim=8|id=796|\"Link,l=13\"))\n",
       "[15] ((dim=2|id=528|\"S=1/2,Site,n=15\"), (dim=2|id=220|\"Link,l=15\"), (dim=4|id=332|\"Link,l=14\"))\n",
       "[16] ((dim=2|id=524|\"S=1/2,Site,n=16\"), (dim=2|id=220|\"Link,l=15\"))\n",
       ")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_s = 16\n",
    "sites = siteinds(\"S=1/2\", N_s)\n",
    "\n",
    "J = 1.0\n",
    "h = 1\n",
    "g = 0.05\n",
    "\n",
    "os = OpSum()\n",
    "for j=1:N_s\n",
    "    if j == N_s\n",
    "        os -= J, \"X\", j, \"X\", 1\n",
    "        os -= g, \"Z\", j, \"Z\", 1\n",
    "    else\n",
    "        os -= J, \"X\", j, \"X\", j+1\n",
    "        os -= g, \"Z\", j, \"Z\", j+1\n",
    "    end\n",
    "    os -= h, \"Z\", j\n",
    "end\n",
    "H = MPO(os, sites)\n",
    "\n",
    "psi0 = randomMPS(sites; linkdims=2^7)\n",
    "\n",
    "nsweeps = 15\n",
    "maxdim = [10,20,100,100,200]\n",
    "cutoff = [1E-10]\n",
    "noise = [1E-6]\n",
    "weight = 50\n",
    "\n",
    "energy0,psi0 = dmrg(H,psi0;nsweeps,maxdim,cutoff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Particle Scattering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "giv_op (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function rz(theta::Float64, i::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    z_i = op(\"Z\", s[i])\n",
    "    Op = exp(-1im/2 * theta * z_i)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end\n",
    "\n",
    "function giv_op(theta::Float64, i::Int, j::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    x_i = op(\"X\", s[i])\n",
    "    y_i = op(\"Y\", s[i])\n",
    "    x_j = op(\"X\", s[j])\n",
    "    y_j = op(\"Y\", s[j])\n",
    "    Op = x_i * y_j - x_j * y_i\n",
    "    Op = exp(1im * theta / 2 * Op)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15-element Vector{Float64}:\n",
       " -0.04452199\n",
       " -0.10805302\n",
       " -0.25917978\n",
       " -0.58569283\n",
       " -1.0800755\n",
       " -1.4472062\n",
       " -1.55743797\n",
       " -1.57020121\n",
       " -1.57078543\n",
       " -1.57079624\n",
       " -1.57079633\n",
       " -1.57079633\n",
       " -1.57079633\n",
       " -1.57079624\n",
       " -1.57078543"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betas_r = [-0.        ,  1.37444679,  2.74889357, -2.15984495, -0.78539816,\n",
    "        0.58904862,  1.96349541, -2.94524311, -1.57079633, -0.19634954,\n",
    "        1.17809725,  2.55254403, -2.35619449, -0.9817477 ,  0.39269908,\n",
    "        1.76714587]\n",
    "thetas_r = [-1.55248274, -1.57065844, -1.5707959 , -1.57079633, -1.5707959 ,\n",
    "       -1.57065844, -1.55248581, -0.78556585, -0.06293259, -0.10815923,\n",
    "       -0.25918264, -0.58569318, -1.0800756 , -1.44720622, -1.55743798]\n",
    "\n",
    "betas_l = [-0.        , -1.37444679, -2.74889357,  2.15984495,  0.78539816,\n",
    "       -0.58904862, -1.96349541,  2.94524311,  1.57079633,  0.19634954,\n",
    "       -1.17809725, -2.55254403,  2.35619449,  0.9817477 , -0.39269908,\n",
    "       -1.76714587]\n",
    "thetas_l = [-0.04452199, -0.10805302, -0.25917978, -0.58569283, -1.0800755 ,\n",
    "       -1.4472062 , -1.55743797, -1.57020121, -1.57078543, -1.57079624,\n",
    "       -1.57079633, -1.57079633, -1.57079633, -1.57079624, -1.57078543]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoff = 1E-8\n",
    "maxdim = 40\n",
    "\n",
    "# Make an array of 'site' indices\n",
    "s = siteinds(psi0)\n",
    "\n",
    "# State Preparation\n",
    "n_kr = 7\n",
    "n_kl = -n_kr\n",
    "sigma = 3/2\n",
    "\n",
    "init_state = deepcopy(psi0)\n",
    "\n",
    "for x in 1:N_s\n",
    "    init_state = rz(betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "for x in 1:N_s-1\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(thetas_r[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "sm = op(\"X\", s[1]) - 1im * op(\"Y\", s[1])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "for x in 1:N_s-1\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(-thetas_r[y], x, x+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:N_s\n",
    "    init_state = rz(-betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "\n",
    "for x in 1:N_s\n",
    "    init_state = rz(betas_l[x], x, init_state, cutoff)\n",
    "end\n",
    "for x in 1:N_s-1\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(thetas_l[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "sm = op(\"X\", s[1]) - 1im * op(\"Y\", s[1])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "for x in 1:N_s-1\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(-thetas_l[y], x, x+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:N_s\n",
    "    init_state = rz(-betas_l[x], x, init_state, cutoff)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.14778769333505076, 0.15610944136797272, 0.31250773503992213, 0.5703412245882167, 0.3125081063220366, 0.15611058253247612, 0.14779083976957574, 0.14737514572740118, 0.1477919537396894, 0.1561107666588773, 0.312508143221159, 0.5703409632250063, 0.3125075456111558, 0.1561090209620497, 0.14778722433782154, 0.14737006650918327]\n"
     ]
    },
    {
     "data": {
      "image/png": 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rX9w3BAAAwCWGbYRVVVU6nW7QoEHcdwMAAMAxhiB0dHQcPHhwTEwM580AAABwjXkb4e7duyMjI8vLy0ePHm12DcKOHTty0hgAAAAXarwwr0KhWL169erVq83GaZpmuSUAAADuMAQhTdOTJ0/Ozc1dt26dn5+fSFRjWAIAALR0DCFXWFh48+bNI0eOTJo0ifuGAAAAuMSws4xcLheJRB4eHtx3AwAAwDGGIFQoFNOmTduzZw/33QAAAHCMefvfkCFDVq1adf/+/TFjxtja2po+9Prrr3PSGAAAABeYg3DNmjWFhYWnT58+ffq02UMIQgAAaE2YgzAlJUWv13PcCgAAAPeYg9DBwYHjPgAAAJoErkcIAAC8xrxG2KVLl0ePHjE+hOsRAgBAa8IchLNmzSorKzPeVavVsbGx9+/fx54yAADQyjAH4apVq8xG9Hr966+/XtNqIgAAQAtV322EAoHgnXfeiY6Ozs3NZbUhAAAALjVgZxkbGxuapvPz89nrBgAAgGP1DcKsrKwlS5ZIJJLOnTuz2hAAAACX6rXXaGVlZXl5uVgs3rRpk1wu56o3AAAA1tVrr1EbGxtvb+8RI0bg8vQAANDK1HevUQAAgFYJZ5YBAABee2aN8KuvviopKan9CcuXL2ezHwAAAE49E4SbN29OT0+v/QkIQgAAaE2eCcLExETGqy+lpqauWbPm5MmT7du356oxAAAALjyzjdDBwcHpWVqtdvPmzUOGDLly5cqmTZvu3bvXVI0CAACwgXmvUUJIaWnpl19+uWHDBp1Ot3DhwnfffdfR0ZHLzgAAADjAEIQajeaHH35YvXp1cXHxyy+/vHbtWg8PD+47AwAA4MAzP41qtdpvv/22Y8eO8+fPHz58eFJS0jfffIMUBACAVuyZNcJhw4b9+eefgwcP3rt3b48ePQghxcXFZk9wcnLirjsAAACWPROEOTk5hJBLly6FhobW9ASaptnuCQAAgDPPBOHy5cvrPKAemtbt27crKystr9O2bVtPT0/L69THnTt3VCpV7XPKy8vrPJ97mzZtfHx8rNcXNL3MzMyCggLL68hksoCAAMvr1EdOTo5VLssqkUiCgoIoirK8FFjomSCcP39+U/UB9ZGRkdE7uK9dh0AL6+i1VVJNSV7mQ2s0VYeysrLAoO4Ofj1qn0bTpPY/CLReX5mbWl6G/6i1KsNHhxdV0kKJ1MI6ZenJN+KvBQZa+tWoj+enTL+bmS+SKSyso8q6d/bUiaFDh1qlK7BEjYdPQDOk1WplbdoXL7tiaaHHOdQng63RUd20Wq1YZmuFnqvU4kXu1ugImpGKKm3Jq4eIu6VXOXX4sK9Wq7VKS3VSa7SlL31L/AZaWMdx6xjOeoba4aTbAADAayyuEZ47d+7o0aP29vZvvPGGt7e32aOpqamHDx9OT09XKBTh4eG17J4DAADAHrbWCI8ePTp16tSAgAC1Wj1gwAClUmk2IT4+vqCgICgoyN7ePjIy8ocffmCpEwAAgFqwtUa4adOmTZs2zZs3jxCSlJS0a9euRYsWmU548cUXX3zxRcNtoVB48ODBuXPnstQMAABATVhZI9RoNFevXg0LCzPcHTly5IULF2qarFKpLl++HBwczEYnAAAAtatxjVCj0SQkJGRnZ5vt1zRlypQ6i+bn59M03aZNG8NdNzc3xsNu4uLiwsPDS0tLQ0NDV69eXVO1Bw8enDhx4urVq4a7Eonkk08+MTvBjVqtFgqFdTbW0qnVaqud0ICmy8vLTSsTYq1TJVSvbDWmlaFZadx30FqfZ5qQiooK048HTTNcUa5RlWmzyozXqmtUabqysrL5fKTLy8tpmhYIWtselBKJRCSq47dP5odjYmJefvnlhw8fVn+oPh9ciURCCDEmqEajsbGxqT4tODg4NTU1Ly8vKioqKirq66+/Zqzm7OzcvXv3F154wXBXIBA4OzsbFmFU0yJaGbNXbRGKMv0Xk0gkhFjrwN7qla2GD+9yC9W476DVPnOESCQS0wasdaA6RSizygJrHQJPUWKxuPl8pLVarY2NTesLwvq8IuYgfOWVV6RS6S+//NKlS5c6s7Q6V1dXiUSSlZVlWG/LyspivKKvSCQyXPVw5cqVL774Yk1B6ODg0KFDh6lTp9ayRKFQyIc1QqFQaMXzUJj+i1n3X4+bytCsNPI7aL3Ps0AgeLYB1iqz2HNTMryDrS8I64Mh5JRK5YMHD86cOTN69OjGFRUIBM8///z+/fu7d++u0WgOHz783nvvEULUavX58+fDwsJsbGxKSkrs7e0N8y9fvuzr69vo1wAAANBoDEFoY2MjEons7OwsqbtmzZqwsLA7d+6kp6e7u7tPnjyZEJKfnz9+/PicnBwPD4+XXnqpsLDQy8srPT09MzPz8OHDliwOAACgcRiCUKFQzJgxY8+ePSEhIY2uGxQUlJKScuHCBQcHh8GDBxtW/9u3b5+YmOjq6koIOXToUHx8fE5OTtu2bfv27SuVWnqyQQAAgEZg3v4XHh6+ePHi9PT08PBwNzc304fqs9eogaOj48SJE01HxGKx4TKHhBCJRDJwoKUn6wMAALAQcxAuXLgwPz//xIkTJ06cMHsI1yMEAIDWhDkI4+LidDodx60AAABwjzkIcflTAADgidqOEbx9+3ZCQkJmZqaHh0dQUFDfvn05awsAAIAbzEFYXl4+c+bMI0eOmA6Ghob+9NNPLi4unDQGAADABeaTCCxatOj48eOrV6++detWUVFRcnLyRx99FB8fjwtEAABAK8OwRqjRaPbs2bN582bjhZOcnZ27du3q7e09ffr0/Pz8tm3bctskAAAAWxjWCAsLC9VqdfXzq40ZM4am6YyMDE4aAwAA4AJDEDo6OopEosTERLNxw4jZ8fUAAAAtGkMQyuXy8ePHv/XWWwcOHDBcSkmv1586dWru3Ln9+/fHkRUAANCaMO8s89VXX3l6ek6bNk0mk7Vr104mk4WHh1MUtWfPHo77AwAAYBXz4RMeHh7Xr18/cuTIpUuX8vLyXFxcQkJCpkyZIpfLOe4PAACAVTUeUC+RSKZOnVr75XABAABaOj5ejBgAAMDoaRAeOHDAw8Nj69athJAePXp41KDpWgUAALC+pz+N+vr6Tp06tVu3boSQF154obS0tOm6AgAA4MjTIOzfv3///v0Nt9etW9dE/QAAAHCKeRvh+vXr09PTzQYzMjLeffdd9lsCAADgDnMQbtu2LTs722wwOzt78+bN7LcEAADAnQbsNVpcXGxvb89eKwAAANx75jjCa9eu/f7774QQlUoVHR194cIF40PFxcU///xzjx49uG4QAACATc8E4cWLF41bAb/66ivTh1xcXIKCgj7//HPuWgMAAGDfMz+NLlq0iKZpmqbbtm176dIl2kRhYWFMTEyvXr2aqlEAAAA2MJ9iLSUlRaFQcNwKAAAA95iD0MHBgeM+AAAAmgTzXqNVVVXvv/9+QECAVCqlnsVxfwAAAKxiXiNcsWLFli1bXnnlFblcbm9vHxIS8uuvv969e3fRokUc9wcAAMAq5jXCnTt3rl+//ptvvunevfvAgQM3btwYHx8/ffr0xMREjvsDAABgFcMaYVFRUXFx8fjx4wkhQqGwvLycECIQCNasWePj45OTk9OuXTuu2wQAAGAHwxqhRCIhhOj1ekKIu7t7ZmamYdzR0ZGm6dzcXC77AwAAYBVDENrZ2bVv3z4pKYkQ0r9//9OnT1+5ckWj0WzcuFEoFPr6+nLeJAAAAFuYd5aZMWNGTEzMtGnTJkyYEBQUNHDgQMP4smXLnJ2dOWwPAACAXcxB+NFHHxluCASC8+fPnzx58uHDh7179x4xYgSHvQEAALCOOQhNSaXSiIgIDloBAADgXo1BqNVqT548eePGjezsbHd396CgoOeff14qlXLZHAAAANuYgzArK2vixIkJCQlCodDZ2bm4uFir1fr5+R07dqxbt24ctwgAAMAe5gPqZ8+enZWVdfDgQbVaXVBQUFFR8euvv+r1+oiICMNhFQAAAK0DQxAqlcrz589//fXXU6ZMEYvFhBChUDh27Ni9e/feuXMnOTmZ8yYBAADYwhCENE0TQgIDA83Gg4KCyP8faA8AANA6MAShi4tL3759jx07ZjZ+7NgxT09PbCMEAIDWhHlnmQ0bNsyaNSsjIyMiIsLd3b2wsPDkyZM7duzYsmVLRkaGYY6rq6udnR2HrQIAAFgfcxDOnj27oKBg27Zt27ZtMx2fMWOG8fb27dvnzZvHbncAAAAsYw7C7du3V1RU1P7Mvn37stAPAAAAp5iDcOLEiRz3AQAA0CSYjyMEAADgCeY1whdffLG4uJjxod9++43NfgAAADhV90m3CSGFhYV37tyRSqXYLggAAK0McxAePHjQbCQvLy8yMnL8+PHstwQAAMCd+m4jdHd3//zzz1esWFFSUsJqQwAAAFxqwM4yXl5eFRUV9+/fr+d8nU53+fLlmJiYyspKxgmPHz+OjY29ePGiSqWqfxsAAABWVK9thAY7d+4khPj4+NRncnl5eVhYmEajsbOzy87Ojo2N9fDwMJ2wa9euhQsXdu/eXafT3bt37/Dhw0OGDGlQ6wAAAJar716jDx48SE1NnTZtmouLS33qfv/99wKB4OrVq0KhcObMmZ988sl//vMf0wn9+/dPS0tzcnIihKxZs2bp0qVXrlxp7KsAAABopPr+NDpo0KDo6Ojo6Oh6zj98+PD06dOFQiEhZNasWYcOHTKb0K1bN0MKEkICAwMfP35cz8oAAABWVN+9RhsqMzPT29vbcNvb2zs7O1uv1wsEDLmr0+m2bt06bdq0mkqVlJRkZmYaWxIKhRMmTDBcKNFIr9fz4fpQer3ecJEsa1VjvN1SKkOz0sjvoNU+ztUbsOY3haUPHk3Tzecj3Vr/ijLmjpkGbCNsEI1GY8wqiUSi0+mqqqpsbGzMptE0/dZbbxFCVqxYUVOpgoKClJQU47lPhULhgAEDnJ2dTedUVlaaRWO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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "magz = expect(init_state, \"Z\")\n",
    "occs = [(1 - magz[n])/2 for n=1:N_s]\n",
    "println(occs)\n",
    "\n",
    "sites = [n for n=1:N_s]\n",
    "plot(bar(sites, occs; label=\"TEBD\"), xlabel=\"site (s)\", ylabel=\"Occupation Number\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96-element Vector{ITensor}:\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=381|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=381|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=381|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=381|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=381|\"S=1/2,Site,n=4\")\n",
       "Dim 2: (dim=2|id=161|\"S=1/2,Site,n=5\")\n",
       "Dim 3: (dim=2|id=381|\"S=1/2,Site,n=4\")'\n",
       "Dim 4: (dim=2|id=161|\"S=1/2,Site,n=5\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ⋮\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=381|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=381|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=381|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=381|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=816|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=816|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999992187501017 + 0.0012499996744791922im  0.0 - 0.0im\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 - 0.0im                    0.0 - 0.0im\n",
       " 0.9999992187501017 - 0.0012499996744791922im  0.0 - 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 - 0.0im  0.9999992187501017 - 0.0012499996744791922im\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 - 0.0im                 0.0 - 0.0im\n",
       " 0.0 - 0.0im  0.9999992187501017 + 0.0012499996744791922im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9996875162757026 + 0.024997395914712332im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                      0.9996875162757026 - 0.024997395914712332im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=584|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=407|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=584|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=407|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.024997395914712332im\n",
       " 0.9996875162757026 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.02499739591471233im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9996875162757026 + 0.0im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make Time-Evolution Gates\n",
    "tau = 0.05\n",
    "N_t = 120\n",
    "\n",
    "gates = ITensor[]\n",
    "for j in 1:N_s\n",
    "    s1 = s[j]\n",
    "    if j == N_s\n",
    "        s2 = s[1]\n",
    "    else\n",
    "        s2 = s[j+1]\n",
    "    end\n",
    "    \n",
    "    x1 = op(\"X\", s1)\n",
    "    x2 = op(\"X\", s2)\n",
    "\n",
    "    hxx = -J * x1 * x2\n",
    "\n",
    "    Gj = exp(-1im * tau * hxx/2)\n",
    "\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    hz = -h * op(\"Z\", s1)\n",
    "    Gj = exp(-1im * tau * hz/2)\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    z1 = op(\"Z\", s1)\n",
    "    z2 = op(\"Z\", s2)\n",
    "\n",
    "    hzz = -g * z1 * z2\n",
    "\n",
    "    Gj = exp(-1im * tau * hzz/2)\n",
    "    push!(gates, Gj)\n",
    "end\n",
    "\n",
    "# Include gates in reverse order too\n",
    "# (N,N-1),(N-1,N-2),...\n",
    "append!(gates, reverse(gates))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635586)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635587)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635593)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635591)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635586)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635582)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635578)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635577)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635584)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635586)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.30023683563558)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.30023683563558)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635577)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n",
      "┌ Warning: Normalization of the density matrix isn't 1 (actual=12.300236835635575)! Be careful!\n",
      "└ @ ITensorEntropyTools /home/michael/.julia/packages/ITensorEntropyTools/SUfxU/src/entropy_calc.jl:22\n"
     ]
    }
   ],
   "source": [
    "function entropy_von_neumann(psi::MPS, b::Int)\n",
    "  s = siteinds(psi)  \n",
    "  orthogonalize!(psi, b)\n",
    "  _,S = svd(psi[b], (linkind(psi, b-1), s[b]))\n",
    "  SvN = 0.0\n",
    "  for n in 1:dim(S, 1)\n",
    "    p = S[n,n]^2\n",
    "    SvN -= p * log(p)\n",
    "  end\n",
    "  return SvN\n",
    "end\n",
    "\n",
    "# Compute and print <Sz> at each time step\n",
    "# then apply the gates to go to the next time\n",
    "maxdim = 40\n",
    "occs = []\n",
    "EEs = []\n",
    "dims = []\n",
    "ttotal = N_t * tau\n",
    "state = init_state\n",
    "for t in 0:tau:ttotal\n",
    "    # println(\"Pass 1\")\n",
    "    Sz = expect(state, \"Z\")\n",
    "    occ = [(1 - Sz[n])/2 for n=1:N_s]\n",
    "    push!(occs, occ)\n",
    "\n",
    "    EE = []\n",
    "    for j in 2:N_s-1\n",
    "      ee = ee_region(state, 1:j)\n",
    "      push!(EE, ee)\n",
    "    end\n",
    "    push!(EEs, EE)\n",
    "    \n",
    "    bond_dim = maxlinkdim(state)\n",
    "    push!(dims, bond_dim)\n",
    "    t ≈ ttotal && break\n",
    "\n",
    "    state = apply(gates, state; cutoff, maxdim)\n",
    "    normalize!(state)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sites = [n for n=1:N_s]\n",
    "# for p in 1:length(occs)\n",
    "#     if (p - 1) % 10 == 0\n",
    "#         plt = plot(bar(sites, occs[p]; label=\"TEBD\"); ylims= (0,0.6), xlabel=\"site\")\n",
    "#         png(plt, \"Plots/plt\" * string(p) * \".png\")\n",
    "#     end\n",
    "# end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "occs_mat = stack(occs, dims=1)\n",
    "\n",
    "heatmap(1:N_s, 0:tau:(N_t*tau), occs_mat, xlabel=\"site (s)\", ylabel=\"time (t)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "title = \"Data/\"\n",
    "title *= \"ising-exact-occs-N_s\" * string(N_s)\n",
    "title *= \"-J\" * string(J)\n",
    "title *= \"-h\" * string(h)\n",
    "title *= \"-g\" * string(g)\n",
    "title *= \"-width\" * string(sigma)\n",
    "title *= \"-dt\" * string(tau) * \".txt\"\n",
    "writedlm(title, occs_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Data/ising-exact-occs-N_s16-J1.0-h1-g0.05-width1.5-dt0.05.txt\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "EEs_mat = stack(EEs, dims=1)\n",
    "title = \"Data/\"\n",
    "title *= \"ising-exact-EEs-N_s\" * string(N_s)\n",
    "title *= \"-J\" * string(J)\n",
    "title *= \"-h\" * string(h)\n",
    "title *= \"-g\" * string(g)\n",
    "title *= \"-width\" * string(sigma)\n",
    "title *= \"-dt\" * string(tau) * \".txt\"\n",
    "writedlm(title, EEs_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Data/ising-exact-EEs-N_s16-J1.0-h1-g0.05-width1.5-dt0.05.txt\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.12.1",
   "language": "julia",
   "name": "julia-1.12"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
